end corrections using 1/4 wave resonator

[blacko2k]

Hi guys,

Im investigating the magnitude of the end corrections of perforate pipes in the context of automotive exhaust silencers.
Unfortunately I've hit problems quite early on: When investigating the natural frequency of my 1/4 wave resonator - initially with no perf pipe at all - the resonant peak is around 180Hz, however it is expected to be around 300Hz.

I've used the fact that: f = 1/4 . c/L (i.e. n = 1)

I have been instructed to "have 1Hz/mm = 1000Hz/m", so therefore found df/dL, and rearranged for L to find the required length of the tube:

L = sqrt (c/4*1000) = 0.293m

Using the equation above, when c = 343 m/s and L = 0.293m the expected response is around 293Hz. Unfortunately I only get an unpronounced, wide response around 170-190Hz, with a smaller unpronounced response around 320Hz.

My set-up involves a 2 inch diameter metal tube. One end has a speaker emmiting white noise. The other end is surrounded by a larger plastic tube, held in place by an wooden ring fitted snugly around the metal tube, which the larger plastic tube sits on:


<--- L=0.293m ---->
-------------------------------------
|
Mic---->|
---------------------------------------
<--sound source ========================>
---------------------------------------
|
|
-------------------------------------

Sorry for the poor diagram, I may be able to upload some sketches if required.

Does anybody have any ideas why I'm not getting the response predicted? Ive surrounded the speaker with foam, and the open end near the speaker (i.e. not the resonator end) to avoid unwanted readings on the mic, but am stuck as to why its not as predicted.
Im not even getting a sharp peak response, let alone at the expected frequency response!

Thanks,

 

[GregLocock]

I think you need to load a sketch up, but what you appear to have drawn is not a quinkie. A quinkie has a rigid end, I think you are driving the closed end.

Why is the mic at the source end of things?

Please post a decent sketch, I can't make head nor tail of what you have at the moment.



Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[blacko2k]

Hi, thanks for the reply, I've attached a quick computer sketch as i dont have a scanner unfortunately. If this isnt clear I'll try uploading a photo.

Im sending a white noise source down the tube and attempting to use the red region in the image as a quarter wave resonator (as it is an open-closed tubed).

Any thoughts as to why I'm not getting the freq. response as expected? When the idea was proposed to me i thought it weird that sound travelling left-right would resonate in the open-closed tube being where it is. Might that be the problem?

 

[GregLocock]

You mic is in the wrong place

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[blacko2k]

Ok thanks, any pointers on where it can be moved to so that this set-up will work?

 

[GregLocock]

The other end. You are detecting the reflected wave, which is interesting, but not directly relevant.

Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[blacko2k]

Hmm, ok. But surely at the closed end the pressure is a maximum and the speed zero? Wouldn't this be the best place to put the mic'?

 

[GregLocock]

It is a fine place to put the mic if you are trying to understand what is going on, but I think it is a lousy place if you are trying to measure the effectiveness of the silencer. The pressure at that point will bear little resemblance to the output of the silencer.


Cheers

Greg Locock

SIGlease see FAQ731-376 for tips on how to make the best use of Eng-Tips.